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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 3, 1999, pp. 713–732
DOI: 10.4171/ZAA/908

Published online: 1999-09-30

A Compactness Criterion of Mixed Krasnoselskii-Riesz Type in Regular ideal Spaces of Vector Functions

Martin Väth[1]

(1) Czech Academy of Sciences, Prague, Czech Republic

We present a compactness criterion in ideal spaces of vector-valued functions. In the case of real functions, the criterion gives a precise formula for the measure of non-compactness. In the Lebesgue-Bochner spaces $L_p(\mathbb R^n, U)$ the result can be interpreted as a Riesz compactness criterion and generalizes a theorem of Orlicz and Szufla.

Keywords: Riesz compactness criterion, Krasnoselkii compactness criterion, ideal spaces, Köthe spaces, Banach function spaces, spaces of measurable functions, vector-valued functions

Väth Martin: A Compactness Criterion of Mixed Krasnoselskii-Riesz Type in Regular ideal Spaces of Vector Functions. Z. Anal. Anwend. 18 (1999), 713-732. doi: 10.4171/ZAA/908